Can the Wealthier Parent Be Ordered to Pay for the Child's College Cost?

Not unless the parents agree. The judge can only order child support for a non-disabled child until the child turns 18 or graduates from high school, unless the parents agree that child support will continue into college. If parents do agree that one parent will pay for college, and the parents write this up into a stipulation and order that is signed by the judge, the judge can enforce the agreement, even if one parent later changes his mind.